The books say that the field-strength Fs at 1km from a 1kW ERP
station is 300mV/m (say -10dBV/m).

DCF39 has an ERP of 40kW (+16dBkW), so the field-strength at
1km is 1.9V/m (+16dB ref 0.3V/m)

The late Reg Edward's "Groundwave3" program gives
the "spreading loss" at 1960 kms (CT1DRP) as -74dB so a
"free-space Fs" of 380uV/m, but other sources ( CCIR ,
John Adcock) suggest 20dB per decade which would give -66dB gives
a free space Fs at 1960km of 900uV/m ( this approx 6dB difference
seems to be something to do with the first 1km as the slope of
Reg's line is 20dB per decade) So I will just use 20dB/decade on
the 1km Fs.

Assume for simplicity that the daytime level +23dBuV/m
(-97dBV/m) and the night-time level is 40dBuV/m (-80dBV/m) These
level taken from the "Average" line on my DCF39 plots
at Brian CT1DRP's QTH in Porto. Taking the second figures there
is a deficit due to "bounce loss" of about 30dB in
daytime and 14dB at night. Assume there are two hops off the
D-layer in daytime and one hop of the bottom of the E-layer at
night. A simple "solution" to that equation would be
about -12dB for an ionospheric "reflection" and -6dB
for a ground "bounce".

I have tried this method out on several paths where I have a
reasonable idea of the field strength and it is not too far out.
I think it is probably pessimistic over water. For instance it
underestimate Joe's VO1NA strength in the UK. This I believe is
nothing to do with the conductivity of sea-water, at least at LF,
but more to do with the comparative "roughness" between
land and water. Thus we could reduce the sea bounce loss to about
1dB per hop, to get a closer figure.

How to use the "thumbnail" approach on other paths.

1. Work out the Fs at one km from the TX by scaling the 0.3V/m
from a 1kW ERP station i.e 1W ERP would give Fs at 1km of
approximately 10mV/m

2. Using the range calulate the spreading loss at a rate of
20dB per decade i.e 10km=-20dB, 100km= -60dB

3. Divide the path into "hops" ...2000km for
darkness, but only 1000km for a daylight path

4. Allow for an extra "hop loss" of 12dB for every
ionospheric "reflection" and 6dB for a land
"bounce", say about 1dB for a sea "bounce".

5 Add up the spreading and hop loss and apply to the Fs at 1km
to find the estimated Fs at the target. As an example, a 2000km
darkness path has one ionospheric "reflection" so
increase the free-space loss by 12dB. A 4000km darkness path has
two ionospheric "reflections" and one ground
"bounce" so increase the free space Fs by 2*12 +6
i.e.30dB.

It is "stupidly" simple but it gives as accurate a
figure as any of these high flown papers do when you consider the
variability due to multipath and geomagnetic disturbances. The
calculation system needs more data to check paths of 6000km and
longer.